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On the Singularity of the Free Energy at a First Order Phase Transition

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Abstract

At first order phase transition the free energy does not have an analytic continuation in the thermodynamical variable, which is conjugate to an order parameter for the transition. This result is proved at low temperature for lattice models with finite range interaction and two periodic ground-states, under the only condition that they satisfy the Peierls condition.

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References

  1. Fisher, M.E.: The Theory of Condensation and the Critical Point. Physics 3, 255–283 (1967)

    Google Scholar 

  2. Isakov, S.N.: Nonanalytic Features of the First Order Phase Transition in the Ising Model. Commun. Math. Phys. 95, 427–443 (1984)

    MathSciNet  Google Scholar 

  3. Isakov, S.N.: Phase Diagrams and Singularity at the Point of a Phase Transition of the First Kind in Lattice Gas Models. Teor. Mat. Fiz. 71, 426–440 (1987)

    MathSciNet  Google Scholar 

  4. Kunz, H., Souillard, B.: Essential Singularity and Asymptotic Behavior of Cluster Size Distribution in Percolation Problems. J. Stat. Phys. 19, 77–106 (1978)

    Google Scholar 

  5. Pfister, C.-E.: Large Deviations and Phase Separation in the Two Dimensional Ising Model. Helv. Phys. Acta 64, 953–1054 (1991)

    MathSciNet  Google Scholar 

  6. Sinai, Ya.G.: Theory of Phase Transitions: Rigorous Results. Oxford: Pergamon Press, 1982

  7. Zahradnik, M.: An Alternate Version of Pirogov-Sinai Theory. Commun. Math. Phys. 93, 559–581 (1984)

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Institut de Théorie des Phénomènes Physiques, EPF-L, 1015, Lausanne, Switzerland

    Sacha Friedli

  2. Institut d’Analyse et de Calcul Scientifique, EPF-L, 1015, Lausanne, Switzerland

    Charles-E. Pfister

Authors
  1. Sacha Friedli
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  2. Charles-E. Pfister
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Corresponding author

Correspondence to Charles-E. Pfister.

Additional information

Communicated by H. Spohn

Supported by Fonds National Suisse de la Recherche Scientifique.

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Friedli, S., Pfister, CE. On the Singularity of the Free Energy at a First Order Phase Transition. Commun. Math. Phys. 245, 69–103 (2004). https://doi.org/10.1007/s00220-003-1003-5

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  • DOI: https://doi.org/10.1007/s00220-003-1003-5

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